Computing Entanglement in Simulations of Quantum Condensed Matter

Abstract

Condensed matter theorists have recently begun exploiting the properties of entanglement as a resource for studying quantum materials. At the forefront of current efforts is the question of how the entanglement of two subregions in a quantum many-body groundstate scales with the subregion size. The general belief is that typical groundstates obey the so-called "area law", with entanglement entropy scaling as the boundary between regions. This has lead theorists to propose that sub-leading corrections to the area law provide new universal quantities at quantum critical points and in exotic quantum phases (i.e. topological Mott insulators). However, away from one dimension, entanglement entropy is difficult or impossible to calculate exactly, leaving the community in the dark about scaling in all but the simplest non-interacting systems. In this talk, I will discuss recent breakthroughs in calculating entanglement entropy in two dimensions and higher using advanced quantum Monte Carlo simulation techniques. We show, for the first time, evidence of leading-order area law scaling in a prototypical model of strongly-interacting quantum spins. This paves the way for future work in calculating new universal quantities derived from entanglement, in the plethora of real condensed matter systems amenable to numerical simulation.